**Contemporary Mathematics**

Volume: 701;
2018;
232 pp;
Softcover

MSC: Primary 11; 14;

Print ISBN: 978-1-4704-1991-2

Product Code: CONM/701

List Price: $117.00

AMS Member Price: $93.60

MAA member Price: $105.30

**Electronic ISBN: 978-1-4704-4385-6
Product Code: CONM/701.E**

List Price: $117.00

AMS Member Price: $93.60

MAA member Price: $105.30

# Number Theory Related to Modular Curves: Momose Memorial Volume

Share this page *Edited by *
*Joan-Carles Lario; V. Kumar Murty*

This volume contains the proceedings of the Barcelona-Boston-Tokyo
Number Theory Seminar, which was held in memory of Fumiyuki Momose, a
distinguished number theorist from Chuo University in Tokyo.

Momose, who was a student of Yasutaka Ihara, made important
contributions to the theory of Galois representations attached to
modular forms, rational points on elliptic and modular curves,
modularity of some families of Abelian varieties, and applications of
arithmetic geometry to cryptography.

Papers contained in this volume cover these general themes in
addition to discussing Momose's contributions as well as recent work
and new results.

#### Readership

Graduate students and research mathematicians interested in number theory and arithmetic geometry.

# Table of Contents

## Number Theory Related to Modular Curves: Momose Memorial Volume

- Cover Cover11
- Title page iii4
- Contents vii8
- Preface ix10
- The Barcelona Conference xi12
- My friend, Fumiyuki Momose xiii14
- An overview of the mathematical work of Fumiyuki Momose 116
- A note on algebraic points on Shimura curves 924
- On quadratic points of classical modular curves 1732
- 1. Introduction 1732
- 2. The set of quadratic points is a not finite set: Hyperelliptic and Bielliptic curves 1934
- 3. Automorphism group of classical modular curves 2338
- 4. Which curves 𝑋₀(𝑁) have an infinite set of quadratic points? 2641
- 5. Other classical modular curves 2843
- Acknowledgements 3348
- References 3348

- 𝑝-adic point counting on singular superelliptic curves 3550
- A refinement of a conjecture of Gross, Kohnen, and Zagier 5368
- A vanishing criterion for Dirichlet series with periodic coefficients 6984
- Rational families of 17-torsion points of elliptic curves over number fields 8196
- An explicit integral representation of Siegel-Whittaker functions on 𝑆𝑝(2,ℝ) for the large discrete series representations 105120
- On implementation of GHS attack against elliptic curve cryptosystems over cubic extension fields of odd characteristic 125140
- The Sato-Tate conjecture for a Picard curve with complex multiplication (with an appendix by Francesc Fité) 151166
- Arithmetic twists and Abelian extensions 167182
- 1. Introduction 167182
- 2. Abelian varieties of type \T 168183
- 3. The arithmetic twisting group 169184
- 4. A general construction 171186
- 5. The ideal 𝑆_{𝑛}(𝐸/𝐹) 174189
- 6. Applications to Abelian varieties 180195
- 7. The 𝑝-part of the conductor 182197
- 8. Numerical examples 185200
- 9. Remarks on other work 190205
- References 190205

- Transcendental numbers and special values of Dirichlet series 193208
- 1. Introduction 193208
- 2. The discovery of transcendental numbers 194209
- 3. An overview of problems and results 197212
- 4. Euler’s theorem revisited 199214
- 5. Special values of Dirichlet 𝐿-series 203218
- 6. Summation of infinite series of rational functions 205220
- 7. Multiple zeta values 206221
- 8. The Chowla-Milnor conjecture 208223
- 9. The Riemann zeta function at odd arguments 209224
- 10. Hecke’s conjecture and the Siegel-Klingen theorem 211226
- 11. Artin 𝐿-series 213228
- 12. Schanuel’s conjecture and special values at 𝑠=1. 213228
- 13. The Chowla and Erdös conjectures 214229
- 14. Concluding remarks 215230
- Acknowledgments 215230
- References 215230

- Back Cover Back Cover1234